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arXiv · 1906.11966

[1,2]-Domination in Generalized Petersen Graphs

Fairouz Beggas·Volker Turau·Mohammed Haddad·Hamamache Kheddouci
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Abstract

A vertex subset $S$ of a graph $G=(V,E)$ is a $[1,2]$-dominating set if each vertex of $V\backslash S$ is adjacent to either one or two vertices in $S$. The minimum cardinality of a $[1,2]$-dominating set of $G$, denoted by $\gamma_{[1,2]}(G)$, is called the $[1,2]$-domination number of $G$. In this paper the $[1,2]$-domination and the $[1,2]$-total domination numbers of the generalized Petersen graphs $P(n,2)$ are determined.

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Fairouz Beggas, Volker Turau, Mohammed Haddad, Hamamache Kheddouci. 2019-06-27. [1,2]-Domination in Generalized Petersen Graphs. https://arxiv.org/abs/1906.11966

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